“I don’t know the word,” Louis van Gaal said, pointing to his forearm. In Amsterdam it is “kippenvel”. Translation: goosebumps. Van Gaal put his chin up, marched down the tunnel and, when he emerged into the fading light, it was with an expression on his face that suggested he liked the look of his new workplace.

They are quickly warming to him, too, judging by the crowd’s acclaim after this slightly eccentric win, and not forgetting the clamour to join in the chain of high fives as he made his way along the touchline early in the second half. David Moyes’s first night as manager at Old Trafford last summer was one to forget, with Sevilla inflicting a 3-1 chasing that turned out to be a sign of things to come.

Sir Alex Ferguson liked to say there was no other side in the world who scored more last-minute winners. Moyes did not experience one. Van Gaal has quickly got in on the act – Fellaini’s shot was the final kick of the night bar the restart – and there was a delicious irony about the fact it came from a player who had been singled out as the scapegoat from the Moyes era.

Fellaini, a second-half substitute, had attracted loud, ironic cheers every time he completed a simple pass. If the feel-good factor is slowly returning to Old Trafford, there was a reminder that Van Gaal is inheriting a club where discontent lingers just beneath the surface. “I cannot change, in three or four weeks, everything,” he said. Yet he did seem relatively happy with what had passed so far. “We have won every game, which is fantastic when you see our opponents.”

Van Gaal certainly sounded like a man who meant business. He also seemed impatient to get started, making his first appearance a full 36 minutes before the kick-off, waving to a mostly deserted Stretford End before striding purposefully across the pitch to observe the warm-up in front of the stand they had named after Ferguson and directly beneath the banner heralding the former manager’s achievements.

In other parts of the ground the branding was all about “Reunited” as if the real United had been away for some time. MUTV, the club’s in-house television channel, has been running an advert over the summer that tells its own story. It shows the Moyes banner – “The Chosen One” – amid a stormy sky and a Scottish voice sounding close to disgusted. “Football, bloody hell. What the hell was that all about?” A woman’s voice is next: “I was ashamed of them.” Then the banner, showing the face of Moyes, crumples and another voice comes in. “Trust me, we’ll be back. A new storm is breaking.” United, under Van Gaal, give the impression they would like to airbrush Moyes from their history.

It will not be that easy, of course, and there were moments when United’s vulnerability in defence briefly seemed like a throwback to last season. Tom Cleverley was at fault for Rodrigo Moreno’s equaliser, with a hashed clearance into his opponent’s path, and a side that had previously looked ripe to be beaten were suddenly threatening to spoil Van Gaal’s evening.

Instead the focus of everyone’s attention was left to congratulate himself on his decision-making – “It was about the substitutes,” Van Gaal volunteered – on an evening when the only real downside for United was the injury bulletin about Luke Shaw, Jonny Evans and Antonio Valencia.

All three might miss Saturday’s game against Swansea, at a time when United are already short of defenders. Tyler Blackett played as the left-sided centre-half alongside Phil Jones and Chris Smalling, with Reece James replacing Shaw as the left wing-back in the 3-4-1-2 system that has been Van Gaal’s stamp since arriving from the World Cup.

The new formation means Juan Mata can play in his best position, with Rooney pushed further forward, partnered here by Javier Hernández because Robin van Persie was not fully fit. Fellaini trotted on after 76 minutes and it soon became apparent he might need selective hearing – but then Blackett sent a long ball into the penalty area. Valencia’s goalkeeper, Diego Alves, got in a tangle with one of his defenders and suddenly Fellaini was rolling the ball into an exposed net and holding up a triumphant fist.